Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment

It is shown that a nonequilibrium environment can be instrumental in suppressing decoherence between distinct decoherence-free subspaces in quantum registers. The effect is found in the framework of exact coherent-product solutions for model registers decohering in a bath of degenerate harmonic modes, through couplings linear in bath coordinates. These solutions represent a natural nonequilibrium extension of the standard solution for a decoupled initial register state and a thermal environment. Under appropriate conditions, the corresponding reduced register distribution can propagate in an unperturbed manner, even in the presence of entanglement between states belonging to distinct decoherence-free subspaces, and despite persistent bath entanglement. As a byproduct, we also obtain a refined picture of coherence dynamics under bang-bang decoherence control. In particular, it is shown that each radio-frequency pulse in a typical bang-bang cycle induces a revival of coherence, and that these revivals are exploited in a natural way by the time-symmetrized version of the bang-bang protocol.